Analysis of the $P_{cs}(4338)$ and related pentaquark molecular states via the QCD sum rules

Abstract

In this work, we tentatively identify the $P_{cs}(4338)$ as the $\bar{D}\Xi_c$ molecular state, and distinguish the isospins of the current operators to explore the $\bar{D}\Xi_c$, $\bar{D}\Lambda_c$, $\bar{D}_s\Xi_c$, $\bar{D}_s\Lambda_c$, $\bar{D}^*\Xi_c$, $\bar{D}^*\Lambda_c$, $\bar{D}^*_s\Xi_c$ and $\bar{D}^*_s\Lambda_c$ molecular states without strange, with strange and with double strange in the framework of the QCD sum rules in details. The present explorations favor identifying the $P_{cs}(4338)$ ($P_{cs}(4459)$) as the $\bar{D}\Xi_c$ ($\bar{D}^*\Xi_c$) molecular state with the spin-parity $J^P={\frac{1}{2}}^-$ (${\frac{3}{2}}^-$) and isospin $(I,I_3)=(0,0)$, the observation of their cousins with the isospin $(I,I_3)=(1,0)$ in the $J/\psi\Sigma^0/\eta_c\Sigma^0$ invariant mass distributions would decipher their inner structures.